1st Edition

Principles of Solid Mechanics

By Rowland Richards, Jr. Copyright 2001

    Evolving from more than 30 years of research and teaching experience, Principles of Solid Mechanics offers an in-depth treatment of the application of the full-range theory of deformable solids for analysis and design. Unlike other texts, it is not either a civil or mechanical engineering text, but both. It treats not only analysis but incorporates design along with experimental observation. Principles of Solid Mechanics serves as a core course textbook for advanced seniors and first-year graduate students.

    The author focuses on basic concepts and applications, simple yet unsolved problems, inverse strategies for optimum design, unanswered questions, and unresolved paradoxes to intrigue students and encourage further study. He includes plastic as well as elastic behavior in terms of a unified field theory and discusses the properties of field equations and requirements on boundary conditions crucial for understanding the limits of numerical modeling.

    Designed to help guide students with little experimental experience and no exposure to drawing and graphic analysis, the text presents carefully selected worked examples. The author makes liberal use of footnotes and includes over 150 figures and 200 problems. This, along with his approach, allows students to see the full range, non-linear response of structures.

    PREFACE
    INTRODUCTION
    Types of Linearity
    Displacements-Vectors and Tensors
    Finite Linear Transformation
    Symmetric and Asymmetric Components
    Principal or Eigenvalue Representation
    Field Theory
    STRAIN AND STRESS
    Deformation (Relative Displacement)
    The Strain Tensor
    The Stress Tensor
    Components at an Arbitrary Orientation (Tensor Transformation)
    Isotropic and Deviatoric Components
    Principal Space and Octahedral Representation
    Two-Dimensional Stress or Strain
    Mohr's Circle for a Plane Tensor
    Mohr's Circle in Three Dimensions
    Equilibrium of a Differential Element
    Other Orthogonal Coordinate Systems
    Summary
    STRESS-STRAIN RELATIONSHIPS (RHEOLOGY)
    Linear Elastic Behavior
    Linear Viscous Behavior
    Simple Viscoelastic Behavior
    Fitting Laboratory Data with Viscoelastic Models
    Elastic-Viscoelastic Analogy
    Elasticity and Plasticity
    Yield of Ductile Materials
    Yield (Slip) of Brittle Materials
    STRATEGIES FOR ELASTIC ANALYSIS AND DESIGN
    Rational Mechanics
    Boundary Conditions
    Tactics for Analysis
    St. Venant's Principle
    Two-Dimensional Stress Formulation
    Types of Partial Differential Field Equations
    Properties of Elliptic Equations
    The Conjugate Relationship between Mean Stress and Rotation
    The Deviatoric Field and Photoelasticity
    Solutions by Potentials
    LINEAR FREE FIELDS
    Isotropic Stress
    Uniform Stress
    Geostatic Fields
    Uniform Acceleration of the Half-Space
    Pure Bending of Prismatic Bars
    Pure Bending of Plates
    TWO-DIMENSIONAL SOLUTIONS FOR STRAIGHT AND CIRCULAR BEAMS
    The Classic Stress-Function Approach
    Airy's Stress Function in Cartesian Coordinates
    Polynomial Solutions and Straight Beams
    Polar Coordinates and Airy's Stress Function
    Simplified Analysis of Curved Beams
    Circular Beams with End Loads
    Concluding Remarks
    RING, HOLES AND INVERSE PROBLEMS
    Lames Solution for Rings under Pressure
    Small Circular Holes in Plates, Tunnels, and Inclusions
    Harmonic Holes and the Inverse Problem
    Harmonic Holes for Free Fields
    Neutral Holes
    Solution Tactics for Neutral Holes-Examples
    Rotating Disks and Rings
    WEDGES AND THE HALF-SPACE
    Concentrated Loadings at the Apex
    Uniform Loading Cases
    Uniform Loading over a Finite Width
    Nonuniform Loadings on the Half-Space
    Line Loads within the Half-Space
    Diametric Loadings of a Circular Disk
    Wedges with Constant Body Forces
    Corner Effects-Eigenfunction Strategy
    TORSION
    Elementary (Linear) Solution
    St. Venant's Formulation (Noncircular Cross-Sections)
    Prandtl's Stress Function
    Membrane Analogy
    Thin-Walled Tubes of Arbitrary Shape
    Hydrodynamic Analogy and Stress Concentration
    CONCEPTS OF PLASTICITY
    Plastic Material Behavior
    Plastic Structural Behavior
    Plastic Field Equations
    Example-Thick Ring
    Limit Load by a "Work" Calculation
    Theorems of Limit Analysis
    The Lower-Bound Theorem
    The Upper-Bound Theorem
    Example-The Bearing Capacity (Indentation) Problem
    ONE-DIMENSIONAL PLASTICITY FOR DESIGN
    Plastic Bending
    Plastic "Hinges"
    Limit Load (Collapse) of Beams
    Limit Analysis of Frames and Arches
    Limit Analysis of Plates
    Plastic Torsion
    Combined Torsion with Tension and/or Bending
    SLIP-LINE ANALYSIS
    Mohr-Coulomb Criterion (Revisited)
    Lateral "Pressures" and the Retaining Wall Problem
    Graphic Analysis and Minimization
    Slip-Line Theory
    Purely Cohesive Materials (f = 0)
    Weightless Materials (g = 0)
    Retaining Wall Solution for f = 0 (EPS Material)
    Comparison to the Coulomb Solution (f = 0)
    Other Special Cases: Slopes and Footings (f = 0)
    Solutions for Weightless Mohr-Coulomb Materials
    The General Case
    An Approximate "Coulomb Mechanism"

    Note: Each chapter also contains a section of Problems and Questions

    Biography

    Rowland Richards Jr.